The idea is demonstrated with a simple example adapted from [1]}. Suppose the true physical system is \(\mu (x) = 4x + x \sin 5x\)  with \(k=1\)  input \(x \in \mathcal {X} = [0,1]\) . The mathematical model is \(\eta (\theta , x) = \theta x\)  with \(p=1\)  calibration parameter \(\theta \in \Theta = \mathbb {R}\) . In this case, \(\theta _{L^2} = 3.565\) . The [2]} estimator is
\(\hat{\theta }_{TW} = 3 \int _0^1 x \hat{\mu }(x) \mathrm {d} x.\) 
